/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/* __ieee754_pow(x,y) return x**y
 *
 *		      n
 * Method:  Let x =  2   * (1+f)
 *	1. Compute and return log2(x) in two pieces:
 *		log2(x) = w1 + w2,
 *	   where w1 has 53-24 = 29 bit trailing zeros.
 *	2. Perform y*log2(x) = n+y' by simulating muti-precision
 *	   arithmetic, where |y'|<=0.5.
 *	3. Return x**y = 2**n*exp(y'*log2)
 *
 * Special cases:
 *	1.  +-1 ** anything  is 1.0
 *	2.  +-1 ** +-INF     is 1.0
 *	3.  (anything) ** 0  is 1
 *	4.  (anything) ** 1  is itself
 *	5.  (anything) ** NAN is NAN
 *	6.  NAN ** (anything except 0) is NAN
 *	7.  +-(|x| > 1) **  +INF is +INF
 *	8.  +-(|x| > 1) **  -INF is +0
 *	9.  +-(|x| < 1) **  +INF is +0
 *	10  +-(|x| < 1) **  -INF is +INF
 *	11. +0 ** (+anything except 0, NAN)               is +0
 *	12. -0 ** (+anything except 0, NAN, odd integer)  is +0
 *	13. +0 ** (-anything except 0, NAN)               is +INF
 *	14. -0 ** (-anything except 0, NAN, odd integer)  is +INF
 *	15. -0 ** (odd integer) = -( +0 ** (odd integer) )
 *	16. +INF ** (+anything except 0,NAN) is +INF
 *	17. +INF ** (-anything except 0,NAN) is +0
 *	18. -INF ** (anything)  = -0 ** (-anything)
 *	19. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
 *	20. (-anything except 0 and inf) ** (non-integer) is NAN
 *
 * Accuracy:
 *	pow(x,y) returns x**y nearly rounded. In particular
 *			pow(integer,integer)
 *	always returns the correct integer provided it is
 *	representable.
 *
 * Constants :
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#include "math_libm.h"
#include "math_private.h"

#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
/* C4756: overflow in constant arithmetic */
#pragma warning ( disable : 4756 )
#endif

#ifdef __WATCOMC__ /* Watcom defines huge=__huge */
#undef huge
#endif

static const double
bp[] = {1.0, 1.5,},
       dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
                dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
                         zero    =  0.0,
                         one	=  1.0,
                         two	=  2.0,
                         two53	=  9007199254740992.0,	/* 0x43400000, 0x00000000 */
                           huge	=  1.0e300,
                              tiny    =  1.0e-300,
                              /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
                              L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
                              L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
                              L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
                              L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
                              L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
                              L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
                              P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
                              P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
                              P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
                              P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
                              P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
                              lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
                              lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
                              lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
                              ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
                              cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
                              cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
                              cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
                              ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
                              ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
                              ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

double attribute_hidden __ieee754_pow(double x, double y)
{
    double z, ax, z_h, z_l, p_h, p_l;
    double y1, t1, t2, r, s, t, u, v, w;
    int32_t i, j, k, yisint, n;
    int32_t hx, hy, ix, iy;
    u_int32_t lx, ly;

    EXTRACT_WORDS(hx, lx, x);
    /* x==1: 1**y = 1 (even if y is NaN) */
    if(hx == 0x3ff00000 && lx == 0) {
        return x;
    }
    ix = hx & 0x7fffffff;

    EXTRACT_WORDS(hy, ly, y);
    iy = hy & 0x7fffffff;

    /* y==zero: x**0 = 1 */
    if((iy | ly) == 0) {
        return one;
    }

    /* +-NaN return x+y */
    if(ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
            iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) {
        return x + y;
    }

    /* determine if y is an odd int when x < 0
     * yisint = 0	... y is not an integer
     * yisint = 1	... y is an odd int
     * yisint = 2	... y is an even int
     */
    yisint  = 0;
    if(hx < 0) {
        if(iy >= 0x43400000) {
            yisint = 2;  /* even integer y */
        }
        else if(iy >= 0x3ff00000) {
            k = (iy >> 20) - 0x3ff;	 /* exponent */
            if(k > 20) {
                j = ly >> (52 - k);
                if((j << (52 - k)) == ly) {
                    yisint = 2 - (j & 1);
                }
            }
            else if(ly == 0) {
                j = iy >> (20 - k);
                if((j << (20 - k)) == iy) {
                    yisint = 2 - (j & 1);
                }
            }
        }
    }

    /* special value of y */
    if(ly == 0) {
        if(iy == 0x7ff00000) {      /* y is +-inf */
            if(((ix - 0x3ff00000) | lx) == 0) {
                return one;  /* +-1**+-inf is 1 (yes, weird rule) */
            }
            if(ix >= 0x3ff00000) {  /* (|x|>1)**+-inf = inf,0 */
                return (hy >= 0) ? y : zero;
            }
            /* (|x|<1)**-,+inf = inf,0 */
            return (hy < 0) ? -y : zero;
        }
        if(iy == 0x3ff00000) {	/* y is  +-1 */
            if(hy < 0) {
                return one / x;
            }
            else {
                return x;
            }
        }
        if(hy == 0x40000000) {
            return x * x;  /* y is  2 */
        }
        if(hy == 0x3fe00000) {	/* y is  0.5 */
            if(hx >= 0) {	/* x >= +0 */
                return __ieee754_sqrt(x);
            }
        }
    }

    ax   = fabs(x);
    /* special value of x */
    if(lx == 0) {
        if(ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
            z = ax;			/*x is +-0,+-inf,+-1*/
            if(hy < 0) {
                z = one / z;  /* z = (1/|x|) */
            }
            if(hx < 0) {
                if(((ix - 0x3ff00000) | yisint) == 0) {
                    z = (z - z) / (z - z); /* (-1)**non-int is NaN */
                }
                else if(yisint == 1) {
                    z = -z;  /* (x<0)**odd = -(|x|**odd) */
                }
            }
            return z;
        }
    }

    /* (x<0)**(non-int) is NaN */
    if(((((u_int32_t)hx >> 31) - 1) | yisint) == 0) {
        return (x - x) / (x - x);
    }

    /* |y| is huge */
    if(iy > 0x41e00000) { /* if |y| > 2**31 */
        if(iy > 0x43f00000) {	/* if |y| > 2**64, must o/uflow */
            if(ix <= 0x3fefffff) {
                return (hy < 0) ? huge * huge : tiny * tiny;
            }
            if(ix >= 0x3ff00000) {
                return (hy > 0) ? huge * huge : tiny * tiny;
            }
        }
        /* over/underflow if x is not close to one */
        if(ix < 0x3fefffff) {
            return (hy < 0) ? huge * huge : tiny * tiny;
        }
        if(ix > 0x3ff00000) {
            return (hy > 0) ? huge * huge : tiny * tiny;
        }
        /* now |1-x| is tiny <= 2**-20, suffice to compute
           log(x) by x-x^2/2+x^3/3-x^4/4 */
        t = x - 1;		/* t has 20 trailing zeros */
        w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
        u = ivln2_h * t;	/* ivln2_h has 21 sig. bits */
        v = t * ivln2_l - w * ivln2;
        t1 = u + v;
        SET_LOW_WORD(t1, 0);
        t2 = v - (t1 - u);
    }
    else {
        double s2, s_h, s_l, t_h, t_l;
        n = 0;
        /* take care subnormal number */
        if(ix < 0x00100000) {
            ax *= two53;
            n -= 53;
            GET_HIGH_WORD(ix, ax);
        }
        n  += ((ix) >> 20) - 0x3ff;
        j  = ix & 0x000fffff;
        /* determine interval */
        ix = j | 0x3ff00000;		/* normalize ix */
        if(j <= 0x3988E) {
            k = 0;  /* |x|<sqrt(3/2) */
        }
        else if(j < 0xBB67A) {
            k = 1;  /* |x|<sqrt(3)   */
        }
        else {
            k = 0;
            n += 1;
            ix -= 0x00100000;
        }
        SET_HIGH_WORD(ax, ix);

        /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
        u = ax - bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
        v = one / (ax + bp[k]);
        s = u * v;
        s_h = s;
        SET_LOW_WORD(s_h, 0);
        /* t_h=ax+bp[k] High */
        t_h = zero;
        SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
        t_l = ax - (t_h - bp[k]);
        s_l = v * ((u - s_h * t_h) - s_h * t_l);
        /* compute log(ax) */
        s2 = s * s;
        r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
        r += s_l * (s_h + s);
        s2  = s_h * s_h;
        t_h = 3.0 + s2 + r;
        SET_LOW_WORD(t_h, 0);
        t_l = r - ((t_h - 3.0) - s2);
        /* u+v = s*(1+...) */
        u = s_h * t_h;
        v = s_l * t_h + t_l * s;
        /* 2/(3log2)*(s+...) */
        p_h = u + v;
        SET_LOW_WORD(p_h, 0);
        p_l = v - (p_h - u);
        z_h = cp_h * p_h;		/* cp_h+cp_l = 2/(3*log2) */
        z_l = cp_l * p_h + p_l * cp + dp_l[k];
        /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
        t = (double)n;
        t1 = (((z_h + z_l) + dp_h[k]) + t);
        SET_LOW_WORD(t1, 0);
        t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
    }

    s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
    if(((((u_int32_t)hx >> 31) - 1) | (yisint - 1)) == 0) {
        s = -one;  /* (-ve)**(odd int) */
    }

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
    y1  = y;
    SET_LOW_WORD(y1, 0);
    p_l = (y - y1) * t1 + y * t2;
    p_h = y1 * t1;
    z = p_l + p_h;
    EXTRACT_WORDS(j, i, z);
    if(j >= 0x40900000) {				/* z >= 1024 */
        if(((j - 0x40900000) | i) != 0) {		/* if z > 1024 */
            return s * huge * huge;  /* overflow */
        }
        else {
            if(p_l + ovt > z - p_h) {
                return s * huge * huge;  /* overflow */
            }
        }
    }
    else if((j & 0x7fffffff) >= 0x4090cc00) {	/* z <= -1075 */
        if(((j - 0xc090cc00) | i) != 0) {	/* z < -1075 */
            return s * tiny * tiny;  /* underflow */
        }
        else {
            if(p_l <= z - p_h) {
                return s * tiny * tiny;  /* underflow */
            }
        }
    }
    /*
     * compute 2**(p_h+p_l)
     */
    i = j & 0x7fffffff;
    k = (i >> 20) - 0x3ff;
    n = 0;
    if(i > 0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
        n = j + (0x00100000 >> (k + 1));
        k = ((n & 0x7fffffff) >> 20) - 0x3ff;	/* new k for n */
        t = zero;
        SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
        n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
        if(j < 0) {
            n = -n;
        }
        p_h -= t;
    }
    t = p_l + p_h;
    SET_LOW_WORD(t, 0);
    u = t * lg2_h;
    v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
    z = u + v;
    w = v - (z - u);
    t  = z * z;
    t1  = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
    r  = (z * t1) / (t1 - two) - (w + z * w);
    z  = one - (r - z);
    GET_HIGH_WORD(j, z);
    j += (n << 20);
    if((j >> 20) <= 0) {
        z = scalbn(z, n);  /* subnormal output */
    }
    else {
        SET_HIGH_WORD(z, j);
    }
    return s * z;
}

/*
 * wrapper pow(x,y) return x**y
 */
#ifndef _IEEE_LIBM
double pow(double x, double y)
{
    double z = __ieee754_pow(x, y);
    if(_LIB_VERSION == _IEEE_ || isnan(y)) {
        return z;
    }
    if(isnan(x)) {
        if(y == 0.0) {
            return __kernel_standard(x, y, 42);  /* pow(NaN,0.0) */
        }
        return z;
    }
    if(x == 0.0) {
        if(y == 0.0) {
            return __kernel_standard(x, y, 20);  /* pow(0.0,0.0) */
        }
        if(isfinite(y) && y < 0.0) {
            return __kernel_standard(x, y, 23);  /* pow(0.0,negative) */
        }
        return z;
    }
    if(!isfinite(z)) {
        if(isfinite(x) && isfinite(y)) {
            if(isnan(z)) {
                return __kernel_standard(x, y, 24);  /* pow neg**non-int */
            }
            return __kernel_standard(x, y, 21); /* pow overflow */
        }
    }
    if(z == 0.0 && isfinite(x) && isfinite(y)) {
        return __kernel_standard(x, y, 22);  /* pow underflow */
    }
    return z;
}
#else
strong_alias(__ieee754_pow, pow)
#endif
libm_hidden_def(pow)
